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'''Author''' : Paolo Oddo 

'''ticket''' : #851

'''Branch''' : [http://forge.ipsl.jussieu.fr/nemo/browser/branches/2011/dev_r2802_INGV4_zdfRic dev_r2802_INGV4_zdfRic ] 
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=== Description ===
In the current version of the Richardson number vertical turbolence scheme eddy viscosities and diffusivities are estimated based on the local gradient Richardson number Ri, using a scheme similar to that of Pacanowski and Philander (1981).


Where Ri(x, y, z, t) is ≥0, 


Av=Abv+ (v0) / (1+αRi)**nn_ri

and

Kv=Kbv + (v0) / (1+ αRi)**(nn_ric+1).


In this shear vertical mixing scheme, the adjustable parameters are:
 the background coefficients, Abv and Kbv;

 the shear eddy viscosity at Ri=0 denoted by v0

 the exponent (nn_ric=2)

 the alpha parameter (5).



This simple scheme has been largely used in numerical models (it is simple and robust) however it does not have any parameterization of the mixing layer.

The basic idea is to introduce near the surface, a mixing-layer model to transfer and dissipate the atmospheric forcings (̌wind-stress and buoyancy flux).

Following the scheme used in HOPS (Harvard Ocean Prediction System) and described in PFJ Lermusiaux (2001) we first evaluate the local depth of turbulent wind-mixing or “Ekman depth” hee(̌x, y, t).


This depth is assumed proportional to the “depth of frictional influence” that is limited by rotation:


hee=Ek u* / f0 		(Rossby and Montgomery, 1935; Cushman-Roisin, 1994).

In this similarity height relationship, the turbulent friction velocity:


u*(x,y)=SQRT(||τ|| / ρ0)


is computed from the wind stress vector τ and reference density ρ0.


The coefficient Ek is an empirical factor (tunable)  and f0 is the Coriolis parameter.


The final he is further constrained by adjustable bounds hemin≤ he ≤ hemax.


Once hee is computed, the vertical eddy coefficients within hee are set to the empirical values Ae and Ke. This vertical mixing-layer model is one of the common results of more complex models (̌e.g. Mofjeld and Lavelle, 1984; Garwood et al., 1985; Stigebrandt, 1985; Large et al., 1994).


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=== Testing ===
Testing could consider (where appropriate) other configurations in addition to NVTK].

||NVTK Tested||!'''YES/NO!'''||
||Other model configurations||!'''YES/NO!'''||
||Processor configurations tested||[ Enter processor configs tested here ]||
||If adding new functionality please confirm that the [[BR]]New code doesn't change results when it is switched off [[BR]]and !''works!'' when switched on||!'''YES/NO/NA!'''||

(Answering UNSURE is likely to generate further questions from reviewers.)

'Please add further summary details here'

 * Processor configurations tested
 * etc----

=== Bit Comparability ===
||Does this change preserve answers in your tested standard configurations (to the last bit) ?||!'''YES/NO !'''||
||Does this change bit compare across various processor configurations. (1xM, Nx1 and MxN are recommended)||!'''YES/NO!'''||
||Is this change expected to preserve answers in all possible model configurations?||!'''YES/NO!'''||
||Is this change expected to preserve all diagnostics? [[BR]]!,,!''Preserving answers in model runs does not necessarily imply preserved diagnostics. !''||!'''YES/NO!'''||

If you answered !'''NO!''' to any of the above, please provide further details:

 * Which routine(s) are causing the difference?
 * Why the changes are not protected by a logical switch or new section-version
 * What is needed to achieve regression with the previous model release (e.g. a regression branch, hand-edits etc). If this is not possible, explain why not.
 * What do you expect to see occur in the test harness jobs?
 * Which diagnostics have you altered and why have they changed?Please add details here........

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=== System Changes ===
||Does your change alter namelists?||!'''YES !'''||
||Does your change require a change in compiler options?||!'''YES/NO !'''||

additional parameters must be included in the corresponding namelist.


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=== Resources ===
!''Please !''summarize!'' any changes in runtime or memory use caused by this change......!''

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=== IPR issues ===
||Has the code been wholly (100%) produced by NEMO developers staff working exclusively on NEMO?||!'''YES/ NO !'''||

If No:

 * Identify the collaboration agreement details
 * Ensure the code routine header is in accordance with the agreement, (Copyright/Redistribution etc).Add further details here if required..........